## Method A: Clinometer

Measurements and Calculations:

Procedure

1. Choose a tree and stand at a distance
away from the tree where the top of the
tree can be seen

2. Direct Clinometer towards the top of the
Tree from the height of the eye

3. Record the angle observed while staying

stationary from the eye to the tip of tree

4. Record the distance at which you are
from the base of the tree

5. Record height of yourself from the base of your feet to your eyeball

6. Repeat steps 2-4 to maximize accuracy of results

7.Organize all data in a table

8. Create a diagram representing you using the clinometer to view the tip of the tree including all measurements recorded previously

9. Put your knowledge of trigonometric ratios to use to calculate the height of tree

Results from Method 1

The first method to measure the height of the tree utilized a basic clinometer. The same person stood at varying distances for three separate trials, resulting in the same height value but a difference in angles and distances from the tree. This led to the observation that as the angle of elevation increased (the angle between the horizontal line of sight and the top of the tree), the distance between the individual and the tree’s base decreased, indicating an inverse relationship between these two variables. The average height of the tree from our values was found to be 550.4 cm or 5.5 metres.

Measurements and Calculations:

Procedure
1. Pick a tree and locate its shadow
2. Measure the tree’s shadow from the base to the longest part of the shadow
3. Ensure that you are on proper level footing for the next steps
6. Repeat steps 3 to 5 for two more people with different heights
7. Organize all the data in a table
8. Create a diagram of two right-angled triangles (one for the tree, one for you)
9. Use your knowledge of similar triangles to find the height of the tree

Results from Method 2

The second method utilized shadows and our knowledge of similar triangles to determine the height of the tree. Each member of the group stood at a uniform distance away from the tree, but because the height of each individual varied, this resulted in varying similar triangles that correspect with the tree.We observed that as the height of the individuals decreased, the length of their shadows also decreased, indicating a direct proportionality between these two variables . As the angle of sunlight remained constant, this allowed us to form similar triangles as the angles of the triangle remained constant.

• We calculated the average height of the
tree from method B to be 543.9 cm or
5.44 m.

Method A: Clinometer